Multiple choice

Let $b = a + c$. Then the equation $ax^2+bx+c=0$ has equal roots, if

  1. $a=c$
  2. $a=-c$
  3. $a=2c$
  4. $a=-2c$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For equal roots, discriminant b^2 - 4ac = 0. Given b = a + c, substitute into the discriminant: (a + c)^2 - 4ac = 0. This is a^2 + 2ac + c^2 - 4ac = 0, which is a^2 - 2ac + c^2 = 0, or (a - c)^2 = 0. Thus, a = c.

AI explanation

For a quadratic equation ax^2 + bx + c = 0 to have equal roots, its discriminant must be zero, meaning b^2 - 4ac = 0. Substituting b = a + c into the condition gives (a + c)^2 - 4ac = 0. Expanding this yields a^2 - 2ac + c^2 = 0, which factors perfectly into (a - c)^2 = 0. Therefore, the equation has equal roots if and only if a = c.

Keep practicing — related questions